Many techniques for transferring information from one location to another include one or more frequency conversion operations. In a transmitting application, for example, a signal carrying information may be upconverted into a radio-frequency (RF) signal for transmission over a medium such as a wireless channel or a conductive or optical cable. In a receiving application, an RF signal carrying information may be received from such a medium and downconverted to an intermediate frequency or to baseband for processing and/or demodulation.
Mixers are commonly used to perform frequency conversion operations. In a typical application, a mixer is arranged to multiply a signal at an initial frequency F0 by a local oscillator (LO) signal to obtain components at the sum and difference frequencies. For example, a quadrature mixing operation may be used to obtain two channels that are 90 degrees out of phase according to an expression such as the following:
                    cos        ⁡                  (                                    ω                              F                ⁢                                                                  ⁢                0                                      ⁢            t                    )                    ⁢              cos        ⁡                  (                                    ω              LO                        ⁢            t                    )                      =                  1        2            ⁢              (                              cos            ⁡                          [                                                (                                                            ω                                              F                        ⁢                                                                                                  ⁢                        0                                                              +                                          ω                      LO                                                        )                                ⁢                t                            ]                                +                      cos            ⁡                          [                                                (                                                            ω                                              F                        ⁢                                                                                                  ⁢                        0                                                              -                                          ω                      LO                                                        )                                ⁢                t                            ]                                      )              ,          ⁢                    cos        ⁡                  (                                    ω                              F                ⁢                                                                  ⁢                0                                      ⁢            t                    )                    ⁢              sin        ⁡                  (                                    ω              LO                        ⁢            t                    )                      =                  1        2            ⁢                        (                                    sin              ⁡                              [                                                      (                                                                  ω                                                  F                          ⁢                                                                                                          ⁢                          0                                                                    +                                              ω                        LO                                                              )                                    ⁢                  t                                ]                                      -                          sin              ⁡                              [                                                      (                                                                  ω                                                  F                          ⁢                                                                                                          ⁢                          0                                                                    -                                              ω                        LO                                                              )                                    ⁢                  t                                ]                                              )                .            The desired one of the two resulting frequency components in each channel may be selected by bandpass filtering the mixer output if necessary.
In a heterodyne circuit, the intermediate frequency (IF) is significantly different from both baseband and RF, such that the conversion between baseband and RF is typically performed in two or more stages. In a homodyne or “zero-IF” circuit, the frequency of the LO signal is substantially equal to the RF, such that the signal is converted between baseband and RF in one stage. In other techniques that are termed “low-IF” or “near-zero-IF”, the IF is close to baseband (e.g., a few hundred kHz or less).